Question

Find the modulus of $\frac{3-4i}{5+7i}$.

Answer 1

Given,

$\frac{3-4i}{5+7i}$

$=\frac{3-4i}{5+7i}\times \frac{5-7i}{5-7i}$

$=\frac{-23-41i}{74}$

$=-\frac{23}{74}-i\frac{41}{74}$

$modulus=\sqrt{{(-\frac{23}{74})}^2+{(-\frac{41}{74})}^2}$

$=\frac{\sqrt{2210}}{74}$